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If ab = b, which of the following must be true?

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If ab = b, which of the following must be true?  [#permalink]

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New post 27 Aug 2018, 01:11
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A
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E

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If ab = b, which of the following must be true?

A) a=1
B) b=0
C) a=1 and b=0
D) a=1 or b=1
E) a=1 or b=0

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Re: If ab = b, which of the following must be true?  [#permalink]

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New post 27 Aug 2018, 01:16
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GMATbuster92 wrote:
if ab=b , which of the following must be true?
A) a=1
B) b=0
C) a=1 and b=0
D) a=1 or b=1
E) a=1 or b=0


\(ab=b........ab-b=0........b(a-1)=0\)
so a=1 or b=0 or both

E
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Re: If ab = b, which of the following must be true?  [#permalink]

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New post 27 Aug 2018, 01:20
fairly straightforward:

ab=b

any number multiplied by 1 remains the same:
1.b=b
--> a=1
there is no other option for a to be anything else since that would modify the outcome

then ask yourself: is there an option where b on it's own can make this true:
the only case where any variable number of times a number = that number is for 0
1.b=b
2.b=b
3.b=b
is only ever true for b=0

since we figured out these 2 requirements a=1, b=0 separately, this means there is no dependency, hence:
OR

a=1 or b=0

--> E

kudos if this helped
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If ab = b, which of the following must be true?  [#permalink]

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New post 04 Mar 2019, 15:29
Hello everyone!

Could someone give some detailed explanation regarding the difference between AND/OR?

\(ab = b\)

\(b (a - 1) = 0\)

\(b = 0\)
\(a = 1\)

Kind regards!
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If ab = b, which of the following must be true?   [#permalink] 04 Mar 2019, 15:29
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